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So I understand the concept of redshift, in that objects traveling away causes their light waves to become stretched, forcing it lower into the electromagnetic spectrum, making it appear 'red'. So does this mean that all waves have a constant 'length' if you will? As in, are waves sort of like a 'string,' in that as they become longer, the total 'length' must remain constant by the height of their amplitudes diminishing?

I hope that was understandable, I'm having a hard time figuring out how to even word the question.

"I'll go," said Chagataev. "But what will I do there? Build socialism?"
"What else?" said the secretary.

You can see the universe expands by analysing the light emitted from stars. The Doppler shift shows that in general everything in the universe is moving away from everything else (with a few exceptions caused by the interplay of gravitational effects from everything else, which is exactly what you'd expect). That is the evidence, and the experiment is happening right now, all the time. We can see it, the theory explains it and predicts the movements that occur.

We don't know what the conditions were before the Big Bang, but it doesn't affect the Big Bang theory. We don't disregard evolution because it doesn't explain how life started. As for why things aren't just moving in an expanding ring from a central point, you seem to have forgotten about gravity. Everything attracts everything else, causing an acceleration that would be in the direction of the net force.

Well... the brain interprets lightwaves of a specific frequency as a specific colour. Each colour has just one frequency.

The velocity of all electromagnetic waves is the speed of light in the medium.

Frequency depends on the speed of the wave and its length. The speed of the wave remains constant. The change in distance between a moving source and a fixed receiver means that the wavelength is altered accordingly: if the source is moving away, the wavelength is increased; towards, and the wavelength is decreased.

The effect has nothing to do with amplitude. Amplitude is related to the energy of the wave. The wavelength, and by extension the frequency, remains constant regardless of amplitude.

Frequency depends on the speed of the wave and its length. The speed of the wave remains constant. The change in distance between a moving source and a fixed receiver means that the wavelength is altered accordingly: if the source is moving away, the wavelength is increased; towards, and the wavelength is decreased.

So does this mean that if you took a two waves from the same source, but millions of light years away, and somehow stretched them so that they were straight lines, they would always be the same length? Meaning that waves always have the same 'total length,' and that by shortening the distance implies 'crunching' them to have shorter wavelength, and increasing the distance implies 'stretching' them for longer?

"I'll go," said Chagataev. "But what will I do there? Build socialism?"
"What else?" said the secretary.

The length of a wave is the distance from peak to peak. For simplicity we'll use a digital wave consisting of one pulse per second with a speed of 1 meter per second, which looks something like this: _|_|_|_|
The wave length is the distance between peaks, from the beginning of one peak to the beginning of the next adjacent peak. This distance is equal to the velocity in meters per second divided by the frequency in pulses per second, which in this case is 1m/s / 1/s = 1 meter.

Now let us start the source moving at a constant speed of 1m/s away from the receiver, which is stationary. The pulses are still being emitted at one second intervals, and travel at one meter per second. So, if you emit a pulse towards the receiver, it will have moved two meters away from the source after one second. This means the wavelength is now two meters, since the next pulse released would be two meters away from the first pulse.

Since the wave moves at a speed of one meter per second, the time between each pulse arriving at the receiver is two seconds, giving a perceived frequency of 0.5 pulses per second. This is the Doppler shift.